Social Ties and the Demand for Financial Services

Butler et al. (2016) highlight financial advice as an important example of a trust-based exchange. In the US, 73% of all retail investors consult a financial advisor before purchasing shares (Hung et al. 2008).

See Disney and Gathergood (2013) for consumer credit products, van Rooij et al. (2011) for stock market participation and Lusardi and Mitchell (2007) for checking and savings accounts, among others.

Most high school students in the U.S. receive a failing grade in financial literacy (Mandell 2008; Markow and Bagnaschi 2005). Similar findings are reported for financial literacy among college students (Chen and Volpe 1998; Shim et al. 2010).

This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the Add Health data files is available on the Add Health website (http://​www.​cpc.​unc.​edu/​addhealth). No direct support was received from grant P01-HD31921 for this analysis.

The limit in the number of nominations is not binding (even by gender). Less than 1% of the students in our sample show a list of ten best friends, both in Wave I and Wave II.

An alternative definition of network link that exploits the direction of the nominations does not substantially change our results.

In Section 4.2, we show that the results remain qualitatively unchanged if we use an alternative definition of weak ties.

Unfortunately, information on the precise timing of the financial decisions is not available in our data. The only existing studies using this information are based on ad hoc survey on small samples (see Varcoe et al. 2010; Danes et al. 1999; Bowen 2002).

PCA uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables (called principal components). This transformation is defined in such a way that the first principal component accounts for the largest portion of variability in the data.

The other existing surveys that report friend nominations are ego-networks. In these surveys, the respondent lists her contacts and some basic characteristics of them (such as gender, education, employment status). Detailed information about nominated contacts is typically not available.

Our results do not depend crucially on these network size thresholds. They remain qualitatively unchanged when changing the network size window slightly. Also, although the computational complexity of the Bayesian analysis prevents us from working with large networks, the IV estimation results remain qualitatively unchanged when using the larger sample of networks between 4 and 400 students (see Section 4.1, and Appendix 2, Tables 12–14).

Spatial models are simultaneous equation models where peers’ behavior depends on own behavior. This implies that \( {\sum }_{j=1}^{n_{r}}g_{ij,r}y_{j,r} \) is correlated with the error term ε _{i, r} in Eq. 1. ML accounts for this simultaneity as it is based on the reduced form. Network fixed effects cannot be included in the model because the group mean \(\overline {y}_{r}\) is not a sufficient statistic for η _r when the adjacency matrix is not row-normalized (see Lee et al. 2010).

See Appendix 1 for more details. For the sake of brevity, the appendix focuses on the case with weak and strong ties. The case with one peer effect is just a special case, that is when ϕ ^S = ϕ ^W .

The kernel densities and the time-series of the values of the chain for the parameters of the control variables are reported in Appendix 2, Figs. 17, 18, 19 and 20.

We compute these estimated probabilities using the marginal effect of an increase of the financial activity index on the probability of adopting each of the different financial services. Marginal effects are evaluated at the sample mean: \(m(\beta )=\phi (\overline {x}\beta )\beta \), where ϕ(⋅) is the normal probability density function. Results do not change significantly if the average of individual marginal effects is instead considered.

For brevity, we do not report the ML estimation results. They are similar to the IV bias-corrected estimation results.

When estimating model (2) including only strong ties (i.e. \( g_{ij,r}^{W}=0\)), we obtain comparable results.

Observe that we model unobserved factors at the individual level. This means that the unobserved factors affecting weak and strong tie formation may be different.

Borrowing from decision theory, we can say that ϕ ^S stochastically dominates ϕ ^W , that is \(P(\phi ^{S}\geq x)\geq P(\phi ^{W}\geq x),\forall x\in \mathbb {R} \) (first-order stochastic dominance). Figure 6 also shows that the distribution of ϕ ^S is negatively (left) skewed. This is due to the condition on the autoregressive parameter in spatial models (peer effect parameter) that guarantees matrix inversion in Model (2). More specifically, the parameter space is (-0.10,0.10) for our network. While this is never binding for ϕ ^W , ϕ ^S is constrained to be below the upper bound. See Appendix 1 for model details.

We show Appendix 2, Table 14 that the results remain qualitatively unchanged if we perform our IV analysis on a larger sample (column 4, Table 2).

The information on parental background in our data is not detailed enough to dig further into the importance of family inputs. For example, information on parental financial literacy or financial decisions are not available.

The Folk Theorem in the repeated game literature (Rubinstein 1979; Fudenberg and Maskin 1986) provides a formal model of personal enforcement, showing that any mutually beneficial outcome can be sustained as a subgame-perfect equilibrium if the same set of agents frequently play the same stage game ad infinitum.

The role of private information in a community of buyers with word-of-mouth communication is also highlighted by Ahn and Suominen M (2001). In this model, buyers receive signals from other agents and adapt their willingness to buy a seller’s product. This mechanism incentivizes the seller to produce high quality output.

See also Greif et al. (1994) for an analysis of the role of bilateral and multilateral reputation mechanisms in the organization of economic transactions.

An alternative measure of network connectivity is the clustering coefficient. While clustering is a node-specific measure, support considers pairs of nodes (link-specific measure). Thus, support is more appropriate in our analysis, which is based on bilateral interaction-types (weak or strong). Observe that networks with an high level of clustering will necessarily display a high fraction of supported links, whereas the converse is not true.

The IV estimates in column (3) of Table 6 are used.

The experiments have also been performed using each outcome separately. The results remain qualitatively unchanged and are available upon request.

The number of shocked agents is chosen in a way such that, for each category of strong ties, we use a numerosity not larger than the real one. In our case, the minimum number of agents for each category of strong ties is 13 (when the number of strong ties is equal to 4). We then shock 13 randomly chosen nodes for each category at each replication. The results, however, remain qualitatively unchanged when changing the number of shocked nodes.

The shock intensity is 2 std points. The results remain qualitatively the same when changing the shock intensity.

We set this number equal to 13, as in our previous exercise. The qualitative results, however, do not depend on this number.

The shocks are symmetrical and equal to +2 std points for agents who have no strong ties and equal to -2 std points for those who do have strong ties.

We set the individual income shock equal to 10 std points, while the shock given to the peers varies from -1 to -20 std points. The qualitative results remain qualitatively unchanged when changing such intensities.

Liu and Lee (2010) also generalize this 2SLS approach to the GMM using additional quadratic moment conditions.

Under some conditions, this 2SLS estimator is robust to the presence of network topology misspecification (see Patacchini and Rainone 2014).

See Tierney (1994) and Chib and Greenberg (1996) for details regarding the resulting Markov chain given by the combination of those two methods.

The algorithm is robust to different starting values (see Chib and Greenberg 1996). However, speed of convergence may increase significantly.

The intuition is that if a tuning parameter is too high, the draws are less likely to be within “high density regions” of the posterior and then rejection is too frequent. The “step” is too long and the chain “does not move enough”. On the other hand if the “step” is too short, the proposal is more likely to be accepted and the chain “moves too much”. Given that we want a mixing chain with a balanced proportion of rejections and acceptances, an optimal step must be chosen. Setting it manually requires a huge amount of time and many manual operations. The dynamic setting of tuning parameters is as follows: where t _A is the acceptance rate at iteration t. The procedure decreases the tuning parameter (the “step”) when proposals are rejected too frequently, while it increases the tuning parameter when proposals are accepted too frequently. This mechanism guarantees a bounded acceptance rate and convergence to optimal tuning.

Given that the rejection rate-based correction of tuning parameters has 0.4 and 0.6 as boundaries, rejection rates oscillate between these values. The likelihood of reaching the boundaries decreases as the number of draws increases and the rejection rates tend to 0.5, as Fig. 10 shows.